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Determination of the Electronic Energy Levels of Colloidal Nanocrystals using Field-Effect Transistors and Ab Initio Calculations Satria Zulkarnaen Bisri, Elena Degoli, Nicola Spallanzani, Gopi Krishnan, Bart Jan Kooi, Corneliu Ghica, Maksym Yarema, Wolfgang Heiss, Olivia Pulci, Stefano Ossicini,* and Maria Antonietta Loi* Inorganic nanoparticles, such as colloidal semiconductor nanocrystals (NCs), are of great interest for their physical properties and for use in device applications, because of their remarkably broad absorption spectra (extending in some cases till the mid-infrared), and their high stability.[1] In colloidal NCs, the surface is passivated with a shell of organic molecules coordinated to the surface allowing an easy dispersion of the material in common solvents and a very precise control of their dimensions during synthesis. Carrier confinement inside semiconducting NCs has a direct effect on the color of the emitted and absorbed light, with the smaller crystals having a wider energy bandgap than the larger ones. This large tunability of their optical properties makes colloidal NCs highly interesting for photovoltaic and optoelectronic device applications. Moreover, semiconducting NCs are promising Dr. S. Z. Bisri,[+] Prof. M. A. Loi Photophysics and Optoelectronics Group Zernike Institute for Advanced Materials University of Groningen, Nijenborgh 4 Groningen, 9747 AG, The Netherlands E-mail: [email protected] Dr. E. Degoli,[+] Prof. S. Ossicini Dipartimento di Scienze e Metodi dell`Ingegneria Università degli Studi di Modena e Reggio Emilia Via Amendola 2 Padiglione Morselli, Reggio Emilia I-42100, Italy E-mail: [email protected] Dr. N. Spallanzani, Prof. O. Pulci ETSF and Dipartimento di Fisica Università degli Studi di Roma Tor Vergata Via della Ricerca Scientifica 1 Rome I-00133, Italy Dr. G. Krishnan, Prof. B. J. Kooi Nanostructured Materials and Interfaces Group Zernike Institute for Advanced Materials University of Groningen, Nijenborgh 4 Groningen, 9747 AG, The Netherlands Dr. C. Ghica National Institute for Materials Physics PO Box MG-7, Bucharest-Magurele 0770125, Romania Dr. M. Yarema, Prof. W. Heiss Institute for Semiconductor and Solid State Physics University of Linz Allenbergerstrasse 69, Linz 4040, Austria [+] These authors contribute equally toward this manuscript.
DOI: 10.1002/adma.201400660
Adv. Mater. 2014, DOI: 10.1002/adma.201400660
materials for exploring new concepts for increasing the photovoltaic efficiency based on multiple exciton generation or carrier multiplication.[2–5] In the case of a narrow bandgap semiconductor such as PbS, the optical bandgap Eoptgap, determined from the first absorption peak maxima, can be enlarged continuously from the bulk value of about 0.4 up to 1.5 eV, depending on the diameter of the NCs,[6–10] thus offering very interesting perspectives for light detection[11–14] and light harvesting.[7,8,11,15–22] In particular in the last case, the separation of electron and hole after photoexcitation is a necessary process. This separation has been attempted with the injection of photoexcited electrons from PbS onto mesoporous SiO2 and TiO2 films,[15–17,19,20] TiO2 nanoparticles,[8,23] C60,[18] and fullerene derivatives.[9,12] In all these cases, the NCs must form a type-II heterostructure with the other material. Thus, it is of fundamental importance to control the energy alignment of the NC’s electronic bandgap with respect to that of the other semiconductor composing the heterojunction. This knowledge will allow tailoring the components of optoelectronic and photovoltaic devices avoiding the trial and error approach. However, this is not a simple task since these energies depend not only on the material, but also on size, shape, and capping agents, which can all introduce shifts in their position. To date, precise measurements of electronic energy levels in semiconductor materials, including colloidal NCs are extremely challenging. For colloidal semiconductors in particular, the current state-of-the-art methods have many limitations, which are aggravated by the presence of ligands on their surface. Ultraviolet photoemission spectroscopy (UPS) for the measurement of the NC’s highest occupied orbital (HOMO),[10,18,24–26] and inverse photoemission spectroscopy (IPES) for the measurement of the NC’s lowest unoccupied orbital (LUMO),[25] are rather imprecise in this case. A similar situation appears for cyclic voltammetry,[8,27,28] and the related cumbersome derivation from tunneling conductance spectra.[29–31] While in the case of CdSe,[27,28] InAs,[29,30] and Si NCs,[24,31] both HOMO energy (through the ionization potential (IP, HOMO = –IP)) and LUMO energy (through the electron affinity (EA, LUMO = –EA)), and thus the electronic (or quasi-particle) bandgap Eqpgap = IP – EA = LUMO – HOMO, have been experimentally determined using the above mentioned methods. For PbS NCs, only either IP,[10] or EA,[8] has been measured. Subsequently, the corresponding EA or IP have been calculated either
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by EA = IP – Eqpgap, or by IP = EA + Eqpgap, choosing different approximations for the electronic bandgap. In this work, we investigate the absolute energy of the LUMO and HOMO energy states, and consequently the electronic bandgap values, for PbS NCs of different sizes, through a combined experimental and theoretical effort. The experimental method relies on the measurement of ambipolar field-effect transistors by using an ionic-liquid-based ion-gel gate.[32–36] This represents the first successful application of this method to an array of fully quantum-confined systems. This method does not only allow the determination of the bandgap but also the higher energy levels of the NC array, which are characterized by slope variation (going true plateau) in the transfer characteristics. Our experimental results are directly compared with results obtained with advanced ab-initio calculations, performed with density functional theory (DFT) using a fully relativistic approach, which allow a direct determination of absolute energy levels. The agreement between measured and calculated energy values is excellent. Finally, this method is very general and easily applicable to all colloidal semiconductors and quantum-confined solids. As stated above, the determination of the NCs’ electronic bandgap requires, with high precision, the knowledge of the absolute position of both the HOMO and LUMO of the NCs with respect to the vacuum, i.e., the IP and the EA, as function of the NCs’ size. The difference between IP and EA gives the Eqpgap, the electronic or quasi-particle bandgap, which is substantially different from the optical bandgap Eoptgap, because the latter also includes the electron-hole interaction. Several approximated approaches to determine the electronic gap have been proposed in the literature of the past few years. Hyun et al.[8] performed cyclic voltammetry on PbS quantum dots of different diameters (from 2.9 to 6.6 nm) and determined the absolute position of the LUMO. The HOMO was then calculated through subtraction from the LUMO, which is not the true Eqpgap, but the optical bandgap Eoptgap determined by the first absorption maximum. Consequently, the HOMO position is overestimated. Jasieniak et al. have determined the absolute position of the HOMO for PbS nanoparticles with diameters ranging from 2.81 to 8.45 nm by using photoelectron spectroscopy in air (PESA).[10] Then, the LUMO was calculated by adding to the HOMO the Eqpgap, calculated as Eoptgap + Jdireh + Jpoleh, that is the sum of the experimentally determined optical bandgap (Eoptgap), the direct Coulomb interaction between a confined electron-hole pair (Jdireh) and the polarization energy (Jpoleh). These summations were provided by an analytical formula, based on effective mass approximation[37] and size-independent dielectric constants. A summary of all these results is depicted in Figure 1a. Here, a novel experimental method to probe the energy levels of colloidal nanocrystal assemblies is proposed. We make use of a new type of field-effect transistor (FET) devices, namely the electric-double-layer (EDL) gated ambipolar transistors (see Figure 1b). The demonstration of ambipolar transistors of colloidal nanocrystal assemblies allows the characterization of both their hole and electron transport.[34,36,38–41] Through the utilization of ionic-liquid-based gating and the related ion gel, a very high carrier density (on the order of 10[14] cm–2) can be accumulated at the semiconductor surface.[32,42] The
2
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Figure 1. (a) The HOMO and LUMO energies of PbS nanocrystals as function of the particle diameter. Red circles: present work ab-initio calculated values for both HOMO and LUMO levels. Red solid lines: fit to a power law of our calculated values (see text). Blue squares: experimental LUMO energies determined by cyclic voltammetry and the corresponding HOMO energies calculated simply subtracting the experimentally determined optical bandgap by Hyun, et al.[8] The blue solid lines are fittings to a power law, calculated by us taking into account their inferred EA value of +4.55 eV for PbS bulk.[8] Black diamonds: experimental HOMO energies determined by PESA and corresponding LUMO energies calculated, as explained in detail within the main text, by Jaseniak et al.[10] The black solid lines are a fit to a power law.[10] (b) Schematic of the ion-gel gated PbS nanocrystal transistor. (c) Stick and ball image of the optimized geometry (after full relaxation) of the spherical Pb68S68 nanocrystal.
accumulated carrier density by this ion gel gating can fill virtually all the available carrier traps, which are estimated to be on the order of 1012–1013 cm–2 in the best colloidal nanocrystal assemblies.[38,41,43,44] Because of the effective trap filling achieved thanks to the gating, it is possible to span the Fermi energy position over a broader energy interval than the HOMO and LUMO gap.[35,45] Through the observation of the current
© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Adv. Mater. 2014, DOI: 10.1002/adma.201400660
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Adv. Mater. 2014, DOI: 10.1002/adma.201400660
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onset in the transistor during gating, the HOMO and LUMO are the dominant parameters that determine the current onset in the ion-gel gated transistors. Therefore, this method can be applied as a tool to probe not only the electronic gap, but in general the energy levels of colloidal nanocrystals and of any nanostructured semiconductor. From a theoretical perspective, it is possible to calculate the electronic bandgap of highly complex systems in a very precise way with the use of ab-initio methods. We therefore apply these advanced computational methods to get information about the size dependence of the ionization potential and the electron affinity for PbS NCs and thus of the quasi-particle bandgap. Since first principles theory can access small nanocrystals (
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Determination of the Electronic Energy Levels of Colloidal Nanocrystals using Field-Effect Transistors and Ab Initio Calculations Satria Zulkarnaen Bisri, Elena Degoli, Nicola Spallanzani, Gopi Krishnan, Bart Jan Kooi, Corneliu Ghica, Maksym Yarema, Wolfgang Heiss, Olivia Pulci, Stefano Ossicini,* and Maria Antonietta Loi* Inorganic nanoparticles, such as colloidal semiconductor nanocrystals (NCs), are of great interest for their physical properties and for use in device applications, because of their remarkably broad absorption spectra (extending in some cases till the mid-infrared), and their high stability.[1] In colloidal NCs, the surface is passivated with a shell of organic molecules coordinated to the surface allowing an easy dispersion of the material in common solvents and a very precise control of their dimensions during synthesis. Carrier confinement inside semiconducting NCs has a direct effect on the color of the emitted and absorbed light, with the smaller crystals having a wider energy bandgap than the larger ones. This large tunability of their optical properties makes colloidal NCs highly interesting for photovoltaic and optoelectronic device applications. Moreover, semiconducting NCs are promising Dr. S. Z. Bisri,[+] Prof. M. A. Loi Photophysics and Optoelectronics Group Zernike Institute for Advanced Materials University of Groningen, Nijenborgh 4 Groningen, 9747 AG, The Netherlands E-mail: [email protected] Dr. E. Degoli,[+] Prof. S. Ossicini Dipartimento di Scienze e Metodi dell`Ingegneria Università degli Studi di Modena e Reggio Emilia Via Amendola 2 Padiglione Morselli, Reggio Emilia I-42100, Italy E-mail: [email protected] Dr. N. Spallanzani, Prof. O. Pulci ETSF and Dipartimento di Fisica Università degli Studi di Roma Tor Vergata Via della Ricerca Scientifica 1 Rome I-00133, Italy Dr. G. Krishnan, Prof. B. J. Kooi Nanostructured Materials and Interfaces Group Zernike Institute for Advanced Materials University of Groningen, Nijenborgh 4 Groningen, 9747 AG, The Netherlands Dr. C. Ghica National Institute for Materials Physics PO Box MG-7, Bucharest-Magurele 0770125, Romania Dr. M. Yarema, Prof. W. Heiss Institute for Semiconductor and Solid State Physics University of Linz Allenbergerstrasse 69, Linz 4040, Austria [+] These authors contribute equally toward this manuscript.
DOI: 10.1002/adma.201400660
Adv. Mater. 2014, DOI: 10.1002/adma.201400660
materials for exploring new concepts for increasing the photovoltaic efficiency based on multiple exciton generation or carrier multiplication.[2–5] In the case of a narrow bandgap semiconductor such as PbS, the optical bandgap Eoptgap, determined from the first absorption peak maxima, can be enlarged continuously from the bulk value of about 0.4 up to 1.5 eV, depending on the diameter of the NCs,[6–10] thus offering very interesting perspectives for light detection[11–14] and light harvesting.[7,8,11,15–22] In particular in the last case, the separation of electron and hole after photoexcitation is a necessary process. This separation has been attempted with the injection of photoexcited electrons from PbS onto mesoporous SiO2 and TiO2 films,[15–17,19,20] TiO2 nanoparticles,[8,23] C60,[18] and fullerene derivatives.[9,12] In all these cases, the NCs must form a type-II heterostructure with the other material. Thus, it is of fundamental importance to control the energy alignment of the NC’s electronic bandgap with respect to that of the other semiconductor composing the heterojunction. This knowledge will allow tailoring the components of optoelectronic and photovoltaic devices avoiding the trial and error approach. However, this is not a simple task since these energies depend not only on the material, but also on size, shape, and capping agents, which can all introduce shifts in their position. To date, precise measurements of electronic energy levels in semiconductor materials, including colloidal NCs are extremely challenging. For colloidal semiconductors in particular, the current state-of-the-art methods have many limitations, which are aggravated by the presence of ligands on their surface. Ultraviolet photoemission spectroscopy (UPS) for the measurement of the NC’s highest occupied orbital (HOMO),[10,18,24–26] and inverse photoemission spectroscopy (IPES) for the measurement of the NC’s lowest unoccupied orbital (LUMO),[25] are rather imprecise in this case. A similar situation appears for cyclic voltammetry,[8,27,28] and the related cumbersome derivation from tunneling conductance spectra.[29–31] While in the case of CdSe,[27,28] InAs,[29,30] and Si NCs,[24,31] both HOMO energy (through the ionization potential (IP, HOMO = –IP)) and LUMO energy (through the electron affinity (EA, LUMO = –EA)), and thus the electronic (or quasi-particle) bandgap Eqpgap = IP – EA = LUMO – HOMO, have been experimentally determined using the above mentioned methods. For PbS NCs, only either IP,[10] or EA,[8] has been measured. Subsequently, the corresponding EA or IP have been calculated either
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by EA = IP – Eqpgap, or by IP = EA + Eqpgap, choosing different approximations for the electronic bandgap. In this work, we investigate the absolute energy of the LUMO and HOMO energy states, and consequently the electronic bandgap values, for PbS NCs of different sizes, through a combined experimental and theoretical effort. The experimental method relies on the measurement of ambipolar field-effect transistors by using an ionic-liquid-based ion-gel gate.[32–36] This represents the first successful application of this method to an array of fully quantum-confined systems. This method does not only allow the determination of the bandgap but also the higher energy levels of the NC array, which are characterized by slope variation (going true plateau) in the transfer characteristics. Our experimental results are directly compared with results obtained with advanced ab-initio calculations, performed with density functional theory (DFT) using a fully relativistic approach, which allow a direct determination of absolute energy levels. The agreement between measured and calculated energy values is excellent. Finally, this method is very general and easily applicable to all colloidal semiconductors and quantum-confined solids. As stated above, the determination of the NCs’ electronic bandgap requires, with high precision, the knowledge of the absolute position of both the HOMO and LUMO of the NCs with respect to the vacuum, i.e., the IP and the EA, as function of the NCs’ size. The difference between IP and EA gives the Eqpgap, the electronic or quasi-particle bandgap, which is substantially different from the optical bandgap Eoptgap, because the latter also includes the electron-hole interaction. Several approximated approaches to determine the electronic gap have been proposed in the literature of the past few years. Hyun et al.[8] performed cyclic voltammetry on PbS quantum dots of different diameters (from 2.9 to 6.6 nm) and determined the absolute position of the LUMO. The HOMO was then calculated through subtraction from the LUMO, which is not the true Eqpgap, but the optical bandgap Eoptgap determined by the first absorption maximum. Consequently, the HOMO position is overestimated. Jasieniak et al. have determined the absolute position of the HOMO for PbS nanoparticles with diameters ranging from 2.81 to 8.45 nm by using photoelectron spectroscopy in air (PESA).[10] Then, the LUMO was calculated by adding to the HOMO the Eqpgap, calculated as Eoptgap + Jdireh + Jpoleh, that is the sum of the experimentally determined optical bandgap (Eoptgap), the direct Coulomb interaction between a confined electron-hole pair (Jdireh) and the polarization energy (Jpoleh). These summations were provided by an analytical formula, based on effective mass approximation[37] and size-independent dielectric constants. A summary of all these results is depicted in Figure 1a. Here, a novel experimental method to probe the energy levels of colloidal nanocrystal assemblies is proposed. We make use of a new type of field-effect transistor (FET) devices, namely the electric-double-layer (EDL) gated ambipolar transistors (see Figure 1b). The demonstration of ambipolar transistors of colloidal nanocrystal assemblies allows the characterization of both their hole and electron transport.[34,36,38–41] Through the utilization of ionic-liquid-based gating and the related ion gel, a very high carrier density (on the order of 10[14] cm–2) can be accumulated at the semiconductor surface.[32,42] The
2
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Figure 1. (a) The HOMO and LUMO energies of PbS nanocrystals as function of the particle diameter. Red circles: present work ab-initio calculated values for both HOMO and LUMO levels. Red solid lines: fit to a power law of our calculated values (see text). Blue squares: experimental LUMO energies determined by cyclic voltammetry and the corresponding HOMO energies calculated simply subtracting the experimentally determined optical bandgap by Hyun, et al.[8] The blue solid lines are fittings to a power law, calculated by us taking into account their inferred EA value of +4.55 eV for PbS bulk.[8] Black diamonds: experimental HOMO energies determined by PESA and corresponding LUMO energies calculated, as explained in detail within the main text, by Jaseniak et al.[10] The black solid lines are a fit to a power law.[10] (b) Schematic of the ion-gel gated PbS nanocrystal transistor. (c) Stick and ball image of the optimized geometry (after full relaxation) of the spherical Pb68S68 nanocrystal.
accumulated carrier density by this ion gel gating can fill virtually all the available carrier traps, which are estimated to be on the order of 1012–1013 cm–2 in the best colloidal nanocrystal assemblies.[38,41,43,44] Because of the effective trap filling achieved thanks to the gating, it is possible to span the Fermi energy position over a broader energy interval than the HOMO and LUMO gap.[35,45] Through the observation of the current
© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Adv. Mater. 2014, DOI: 10.1002/adma.201400660
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Adv. Mater. 2014, DOI: 10.1002/adma.201400660
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onset in the transistor during gating, the HOMO and LUMO are the dominant parameters that determine the current onset in the ion-gel gated transistors. Therefore, this method can be applied as a tool to probe not only the electronic gap, but in general the energy levels of colloidal nanocrystals and of any nanostructured semiconductor. From a theoretical perspective, it is possible to calculate the electronic bandgap of highly complex systems in a very precise way with the use of ab-initio methods. We therefore apply these advanced computational methods to get information about the size dependence of the ionization potential and the electron affinity for PbS NCs and thus of the quasi-particle bandgap. Since first principles theory can access small nanocrystals (
